Finite Group Databasebeta

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D17×D315 #36339258

order21420
automorphism?
homologyAbelianization (H1) = C22 · Schur multiplier (H2) = C2

Aliases

direct productD17×D315
unambiguous semidirect product(C5×D17)⋊D63
unambiguous semidirect product(C7×D17)⋊D45
unambiguous semidirect product(C9×D17)⋊D35

Splittings

Fitting, derived, HallC5×C7×C9×C17 ⋊ C22
HallC7×C9×C17 ⋊ C2×D5
HallC5×C9×C17 ⋊ C2×D7
HallC5×C7×C17 ⋊ C2×D9
HallC5×C7×C9 ⋊ C2×D17
HallC9×C17 ⋊ C2×D35
HallC7×C17 ⋊ C2×D45
HallC5×C17 ⋊ C2×D63
HallC7×C9 ⋊ D5×D17
HallC5×C9 ⋊ D7×D17
HallC5×C7 ⋊ D9×D17
SylowC17 ⋊ C2×D315
SylowC9 ⋊ D17×D35
SylowC7 ⋊ D17×D45
SylowC5 ⋊ D17×D63

Subgroups

subgroupG/H
center, hypercenterC1G
commutator, Fitting, cosocle, hypocenterC5×C7×C9×C17C22
FrattiniC3D17×D105
socleC3×C5×C7×C17C2×D3
LCSG ▷ C5×C7×C9×C17
UCSC1

120 conjugacy classes of subgroups; only the 40 normal subgroups are shown.

normal subgroups only

This group has 120 conjugacy classes of subgroups — too many to draw. Only its 40 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Full subgroup data →

Presentation

transitive degreeμt(G) = 5355

Conjugacy classes & character table

1590 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(21420, 90);